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<geek alert>
Seeing the recent threads reminded me of an exercise I did a while ago in the same vein. I guessed that, however many climbers had achieved one grade, roughly half as many would have achieved the grade above. I started looking at the figures and while for most grades this seemed likely enough it looked like this relationship broke down at higher grades, where the proportion seemed much less than half. So I tinkered with the formulae and came up with a smooth curve that showed half as many climbers per grade at common grades but reached a tenth as many at the highest grade. The actual formula is that there are 10 times as many climbers at the 2nd highest grade as at the highest, and if the proportion of climbers at grade x as compared to grade (x+1) is n then the proportion at grade (x-1) as compared to x is (n/2)+1.
I also began the curve at HVS as I was interested in modelling grade progression and the figures would be very different where most were likely to be very occasional climbers or relative novices.
Since HVS is commonly guessed to be the average grade attained in the UK I theorised that the number of climbers achieving less than this would be roughly equal to those achieving more, thus giving me a total number of climbers and hence percentages at each grade.
The figures themselves came out as:
grade proportion no. climbers percentage
HVS 2.007813 145914 33.9458%
E1 2.015625 72673 16.9068%
E2 2.031250 36055 8.3879%
E3 2.062500 17750 4.1294%
E4 2.125000 8606 2.0021%
E5 2.250000 4050 0.9422%
E6 2.500000 1800 0.4188%
E7 3.000000 720 0.1675%
E8 4.000000 240 0.0558%
E9 6.000000 60 0.0140%
E10 10.000000 10 0.0023%
E11 n/a 1 0.0002%
Not wanting to get into a grade debate about the very hardest routes, it seems to me like the numbers from E6 or so upwards may not be so far off, especially when the old sport conversion (E7=8a, E8=8b, etc.) is used, although all the numbers may be a little on the low side. This also gives the total number of climbers as 429,844, which also sounds credible.
All of which leads me to think that the proportions at each grade may be fair estimates, i.e. that 0.17% of active climbers have climbed E7/8a and that 2% of climbers have climbed E4/7a.
Any further questions? No, I thought not
</geek alert>
Seeing the recent threads reminded me of an exercise I did a while ago in the same vein. I guessed that, however many climbers had achieved one grade, roughly half as many would have achieved the grade above. I started looking at the figures and while for most grades this seemed likely enough it looked like this relationship broke down at higher grades, where the proportion seemed much less than half. So I tinkered with the formulae and came up with a smooth curve that showed half as many climbers per grade at common grades but reached a tenth as many at the highest grade. The actual formula is that there are 10 times as many climbers at the 2nd highest grade as at the highest, and if the proportion of climbers at grade x as compared to grade (x+1) is n then the proportion at grade (x-1) as compared to x is (n/2)+1.
I also began the curve at HVS as I was interested in modelling grade progression and the figures would be very different where most were likely to be very occasional climbers or relative novices.
Since HVS is commonly guessed to be the average grade attained in the UK I theorised that the number of climbers achieving less than this would be roughly equal to those achieving more, thus giving me a total number of climbers and hence percentages at each grade.
The figures themselves came out as:
grade proportion no. climbers percentage
HVS 2.007813 145914 33.9458%
E1 2.015625 72673 16.9068%
E2 2.031250 36055 8.3879%
E3 2.062500 17750 4.1294%
E4 2.125000 8606 2.0021%
E5 2.250000 4050 0.9422%
E6 2.500000 1800 0.4188%
E7 3.000000 720 0.1675%
E8 4.000000 240 0.0558%
E9 6.000000 60 0.0140%
E10 10.000000 10 0.0023%
E11 n/a 1 0.0002%
Not wanting to get into a grade debate about the very hardest routes, it seems to me like the numbers from E6 or so upwards may not be so far off, especially when the old sport conversion (E7=8a, E8=8b, etc.) is used, although all the numbers may be a little on the low side. This also gives the total number of climbers as 429,844, which also sounds credible.
All of which leads me to think that the proportions at each grade may be fair estimates, i.e. that 0.17% of active climbers have climbed E7/8a and that 2% of climbers have climbed E4/7a.
Any further questions? No, I thought not
</geek alert>
In reply to john arran:
Oh John, please go away with your rational thought, hypotheses, and numbers. This is an internet forum for crying out loud! We all know that the *true* state of affairs can only be extrapolated from *my* personal experience!
:P
Oh John, please go away with your rational thought, hypotheses, and numbers. This is an internet forum for crying out loud! We all know that the *true* state of affairs can only be extrapolated from *my* personal experience!
:P
Post edited at 08:55
In reply to john arran:
What are the errors? My old lab supervisor would beat me to death for using that many significant figures (spurious precision!) with no error analysis!
What are the errors? My old lab supervisor would beat me to death for using that many significant figures (spurious precision!) with no error analysis!
Post edited at 08:59
In reply to davidbeynon:
They were just put in to keep the formatting of the columns vaguely legible without being able to use tables or tabs!
Errors are numerous as it's all educated guesswork.
> My old lab supervisor would beat me to death for using that many significant figures (spurious precision!) with no error analysis!
They were just put in to keep the formatting of the columns vaguely legible without being able to use tables or tabs!
Errors are numerous as it's all educated guesswork.
In reply to john arran:
Interesting. But the question as I first read it 'What percentage of climbers climb?' (without the ellipsis) seems like the more interesting philosophical question
Interesting. But the question as I first read it 'What percentage of climbers climb?' (without the ellipsis) seems like the more interesting philosophical question
In reply to john arran:
You can get a lower bound from the number of climbers, and the number in each bin.
[edit] I'm not actually interested in the answer, but the "I thought not" is a clear challenge
You can get a lower bound from the number of climbers, and the number in each bin.
[edit] I'm not actually interested in the answer, but the "I thought not" is a clear challenge
Post edited at 09:08
In reply to john arran:
I would be interested in seeing the plot.
Have you tested this on real data (e.g. the graphs on UKC) or is this completely theoretical?
I would be interested in seeing the plot.
Have you tested this on real data (e.g. the graphs on UKC) or is this completely theoretical?
In reply to davidbeynon:
Are you suggesting Poissonian errors are appropriate here?
> You can get a lower bound from... the number in each bin.
Are you suggesting Poissonian errors are appropriate here?
In reply to kylo-342:
The plot looks like a steep exponential decay.
No real data used - I've never seen any real data about climbing populations that isn't rife with difficulties in interpretation. I do feel though that if the numbers at the higher grades are in the right ballpark and the total number is in the right ballpark, then any reasonably-fitting curve to these points should give you broadly similar percentages. Even if they may be out by a factor of 5 that's still a much smaller variance than the guesses on the other threads!
The plot looks like a steep exponential decay.
No real data used - I've never seen any real data about climbing populations that isn't rife with difficulties in interpretation. I do feel though that if the numbers at the higher grades are in the right ballpark and the total number is in the right ballpark, then any reasonably-fitting curve to these points should give you broadly similar percentages. Even if they may be out by a factor of 5 that's still a much smaller variance than the guesses on the other threads!
In reply to john arran:
Fun but futile. Some issues. Grades are not consistent. Grade widths are not uniform. Performance over time isnt uniform. Most, serious climbers will have onsighted up to E2 (like me for instance, yet Im really a VS leader). Most, ascents over mid extreme are head points.)
Fun but futile. Some issues. Grades are not consistent. Grade widths are not uniform. Performance over time isnt uniform. Most, serious climbers will have onsighted up to E2 (like me for instance, yet Im really a VS leader). Most, ascents over mid extreme are head points.)
In reply to john arran:
Popping a log scale on y suggests it's roughly an exponential dropoff until around E6, then things tail off fast.
http://www.spectral3d.co.uk/misc/grades_log.png
Popping a log scale on y suggests it's roughly an exponential dropoff until around E6, then things tail off fast.
http://www.spectral3d.co.uk/misc/grades_log.png
In reply to Offwidth:
Good points but:
I'm talking about hardest ever leads, which are mostly likely to be on the soft side and mostly likely to be head/redpointed, so reasonably consistent in the circumstances. Different-size grades would also give only a small percentage error.
Would be good to try to estimate some error likelihoods but I've already spent too long on this when I'm supposed to be working! My hunch is that errors are likely to be low single figure multiples, i.e. figures may be 3 times too high or too low.
Good points but:
I'm talking about hardest ever leads, which are mostly likely to be on the soft side and mostly likely to be head/redpointed, so reasonably consistent in the circumstances. Different-size grades would also give only a small percentage error.
Would be good to try to estimate some error likelihoods but I've already spent too long on this when I'm supposed to be working! My hunch is that errors are likely to be low single figure multiples, i.e. figures may be 3 times too high or too low.
In reply to john arran:
Quiet evening in Myanmar?
So - do your figures suggest that 66% climbers operate at HVS and above and 34% at VS and below? (Not too hot on stats, as you can probably tell!)
Chris
Quiet evening in Myanmar?
So - do your figures suggest that 66% climbers operate at HVS and above and 34% at VS and below? (Not too hot on stats, as you can probably tell!)
Chris
In reply to john arran:
If the shape of that plot matches the real world then you could argue that bryond around E7 things are consistently undergraded, and that what is currently E9-10 could reasonably be given E12 or E13.
This "VS on a good day" climber isn't going to go there though.
If the shape of that plot matches the real world then you could argue that bryond around E7 things are consistently undergraded, and that what is currently E9-10 could reasonably be given E12 or E13.
This "VS on a good day" climber isn't going to go there though.
Post edited at 09:35
In reply to Chris Craggs:
Roughly yes, but we're talking about "have succeeded on" rather than "operate at"
Roughly yes, but we're talking about "have succeeded on" rather than "operate at"
In reply to SteveRi:
If the question was "what percentage of 'climbers' on UKC climb" I would guess the answer to that would be 50%!
If the question was "what percentage of 'climbers' on UKC climb" I would guess the answer to that would be 50%!
In reply to john arran:
Before any of these questions can be answered it is surely necessary to define the terms 'climb' and 'climber'. For instance when does a hill walker become a climber? Is everyone who has plodded up Mont Blanc a climber? Indeed does the ascent of an indoor wall, per se, qualify as a 'climb'?
Possibly worth a debate in its own right?
Before any of these questions can be answered it is surely necessary to define the terms 'climb' and 'climber'. For instance when does a hill walker become a climber? Is everyone who has plodded up Mont Blanc a climber? Indeed does the ascent of an indoor wall, per se, qualify as a 'climb'?
Possibly worth a debate in its own right?
In reply to davidbeynon:
Id predict the opposite. Many of the very hardest grades will drop a little with time and traffic and a few HVS climbs will become E2. Plenty of E1s give me a fun experience when Im going well but I am now very very careful on obscure VS onsights on the peak moors, yorkshire and the county.
Id predict the opposite. Many of the very hardest grades will drop a little with time and traffic and a few HVS climbs will become E2. Plenty of E1s give me a fun experience when Im going well but I am now very very careful on obscure VS onsights on the peak moors, yorkshire and the county.
In reply to SteveRi:
Funny but bollocks of course. More like they talk more or harder than they climb.
Funny but bollocks of course. More like they talk more or harder than they climb.
In reply to davidbeynon:
I suspect that a more realistic curve would be roughly Normal, with HVS or so at the centre, as vanishingly few 'climbers' (sorry Dave, still being wooly with definitions!) will have as a hardest ever lead a route graded Easy or Moderate. Indeed the graph from my figures doesn't look too far off a Normal curve above E1 or so.
> If the shape of that plot matches the real world then you could argue that bryond around E7 things are consistently undergraded, and that what is currently E9-10 could reasonably be given E12 or E13.
I suspect that a more realistic curve would be roughly Normal, with HVS or so at the centre, as vanishingly few 'climbers' (sorry Dave, still being wooly with definitions!) will have as a hardest ever lead a route graded Easy or Moderate. Indeed the graph from my figures doesn't look too far off a Normal curve above E1 or so.
In reply to Dave Musgrove:
Even before that, what about the debate around "have succeeded on"? Led on-sight, led with beta, followed, top-roped, dogged, worked to death?
Call me old fashioned (!) but I think the grade you "climb at" is the grade you can on-sight, in a new area, on any kind of rock - more or less!
Chris
> Before any of these questions can be answered it is surely necessary to define the terms 'climb' and 'climber'. For instance when does a hill walker become a climber? Is everyone who has plodded up Mont Blanc a climber? Indeed does the ascent of an indoor wall, per se, qualify as a 'climb'?
> Possibly worth a debate in its own right?
Even before that, what about the debate around "have succeeded on"? Led on-sight, led with beta, followed, top-roped, dogged, worked to death?
Call me old fashioned (!) but I think the grade you "climb at" is the grade you can on-sight, in a new area, on any kind of rock - more or less!
Chris
In reply to john arran:
Grab the stats for the lower grades and I will feed em into gnuplot.
[edit] Hypothesis: The lower grades will be under reported.
Grab the stats for the lower grades and I will feed em into gnuplot.
[edit] Hypothesis: The lower grades will be under reported.
Post edited at 10:07
In reply to davidbeynon:
I had a bash at this several years ago, before all the maths fell out of my head, and concluded that it was effectively a normal distribution, albeit with a bit of positive skew to allow for the fact that the grading series has a definite lower limit, but theoretically unlimited higher values. Centred on about HVS (this was long enough ago that The Dawes was almost singlehandedly providing the skew).
But.
More importantly, your graph appears to plot x-values as E grades. You've included a plot for x= 0, ie E0. There'll be letters.....
Martin (E4. Four occasions. Definitely not in the 98th percentile)
> Without error bars
I had a bash at this several years ago, before all the maths fell out of my head, and concluded that it was effectively a normal distribution, albeit with a bit of positive skew to allow for the fact that the grading series has a definite lower limit, but theoretically unlimited higher values. Centred on about HVS (this was long enough ago that The Dawes was almost singlehandedly providing the skew).
But.
More importantly, your graph appears to plot x-values as E grades. You've included a plot for x= 0, ie E0. There'll be letters.....
Martin (E4. Four occasions. Definitely not in the 98th percentile)
In reply to maisie:
Well, the numbers started at HVS, so I gave that 0 which made all the others correctly numbered.
I think I can label the grades correctly in gnuplot, but life is too short to read the manual and figure out how to do it!
Well, the numbers started at HVS, so I gave that 0 which made all the others correctly numbered.
I think I can label the grades correctly in gnuplot, but life is too short to read the manual and figure out how to do it!
In reply to john arran:
My impression of the crags in the UK is that apart from Stanage they are deserted most of the time. Hardly anything above vs attempted particularly in the mountains. People who climb F6b indoors lead hard severe outdoors. The real issue is getting people back on the crags with a good on sight attitude. Many starred routes have become unclimbable due to neglect. The grade debate hides this fundamental problem.
My impression of the crags in the UK is that apart from Stanage they are deserted most of the time. Hardly anything above vs attempted particularly in the mountains. People who climb F6b indoors lead hard severe outdoors. The real issue is getting people back on the crags with a good on sight attitude. Many starred routes have become unclimbable due to neglect. The grade debate hides this fundamental problem.
In reply to john arran:
I was sure that in the readership survey there had been a question about climbing grades. But it seems that I'm wrong. Then I thought I remember Alan mentioning that according to UKC logbooks, the average grade is HS. Then I found this:
http://www.ukclimbing.com/logbook/graphs.html
Which is all graphs for all users:
"Users have 3,078,256 ticks in their logbooks.
Climbs database lists 275,126 climbs on 18,193 different crags in the UK and around the world."
and since 2002 it's been HS. And with sport it's 6a+
Year Climbs Avg Max
2013 204,458 HS 5.14b
2014 19,719 HS E9
So I think the above curves might need some tweaking.
I was sure that in the readership survey there had been a question about climbing grades. But it seems that I'm wrong. Then I thought I remember Alan mentioning that according to UKC logbooks, the average grade is HS. Then I found this:
http://www.ukclimbing.com/logbook/graphs.html
Which is all graphs for all users:
"Users have 3,078,256 ticks in their logbooks.
Climbs database lists 275,126 climbs on 18,193 different crags in the UK and around the world."
and since 2002 it's been HS. And with sport it's 6a+
Year Climbs Avg Max
2013 204,458 HS 5.14b
2014 19,719 HS E9
So I think the above curves might need some tweaking.
In reply to caradoc:
Really?!??
Every time i've been to the following crags, they have been busy across the grades:
Millstone
Birchen
Lawrencefield
Sennen
Bosigran
Cromlech
Tremadog (all)
Anywhere on slate
Trowbarrow
Ilkley
Grochan
Burbage
Roaches
Really?!??
Every time i've been to the following crags, they have been busy across the grades:
Millstone
Birchen
Lawrencefield
Sennen
Bosigran
Cromlech
Tremadog (all)
Anywhere on slate
Trowbarrow
Ilkley
Grochan
Burbage
Roaches
In reply to maisie:
>ie E0. There'll be letters.....
Darn you beat me to it. I was going to be less subtle as well!
>ie E0. There'll be letters.....
Darn you beat me to it. I was going to be less subtle as well!
In reply to Blue Straggler:
I thought E0 was the grade for Three Pebble Slab....got to go, I can here a mob assembling
I thought E0 was the grade for Three Pebble Slab....got to go, I can here a mob assembling
In reply to mattrm:
Note that my estimates were for hardest ever leads whereas the figures you're quoting are for average grade climbed. I would think a 2 grade difference between hardest and usual would if anything be on the low side.
> Year Climbs Avg Max
> 2013 204,458 HS 5.14b
> 2014 19,719 HS E9
> So I think the above curves might need some tweaking.
Note that my estimates were for hardest ever leads whereas the figures you're quoting are for average grade climbed. I would think a 2 grade difference between hardest and usual would if anything be on the low side.
In reply to Chris Craggs:
I think John wanted to include all grades rather than 'just' up to E8.
> Even before that, what about the debate around "have succeeded on"? Led on-sight, led with beta, followed, top-roped, dogged, worked to death?
> Call me old fashioned (!) but I think the grade you "climb at" is the grade you can on-sight, in a new area, on any kind of rock - more or less!
>
>
I think John wanted to include all grades rather than 'just' up to E8.
In reply to john arran:
There will be loads of people who don't consider themselves climbers (so not in your half million or so total) who will have done things like A'Chir, Curved Ridge or the Inn Pinn, so hardest route Mod, plus plenty who have "done a bit of climbing" who would peak at maybe V Diff or Severe, which might explain your figure of only a third in the lower grades. However I think you're still underestimating the numbers who never climb above VS. Look at any crag with a big grade spread on a sunny day and the busy routes are the Severes and VSs.
There will be loads of people who don't consider themselves climbers (so not in your half million or so total) who will have done things like A'Chir, Curved Ridge or the Inn Pinn, so hardest route Mod, plus plenty who have "done a bit of climbing" who would peak at maybe V Diff or Severe, which might explain your figure of only a third in the lower grades. However I think you're still underestimating the numbers who never climb above VS. Look at any crag with a big grade spread on a sunny day and the busy routes are the Severes and VSs.
In reply to john arran:
A nicely executed theory.
A couple of confounders:
Firstly, the structure you apply assumes that grades are evenly-distributed - i.e. that there is the same gap HVS to E1 as from E6 to E7. I don't think that's true - in fact I think the "real" difficulty gap may be smaller further up but, because it's closer to the limit (a bit like measuring 1/1000ths of a second for pro sprinters instead of 1/10ths for amateurs).
Secondly, even if they were evenly spaced, the movement between them gets progressivly harder (think 10-minute miles to 5-minute miles).
Thirdly, I think the mix of people changes - from occasional weekend bumblies through to full-time professionals. Once people are in the E6+ arena, they are generally hugely motivated by climbing and also by the aim to get to the next level. Whereas others further down are very happy to bimble on HVS/E1 for the rest of their climbing careers.
Taking the above, I'd suggest that at least the 4th significant figure of your analysis may not be very significant...and probably the third, second and first too!
A nicely executed theory.
A couple of confounders:
Firstly, the structure you apply assumes that grades are evenly-distributed - i.e. that there is the same gap HVS to E1 as from E6 to E7. I don't think that's true - in fact I think the "real" difficulty gap may be smaller further up but, because it's closer to the limit (a bit like measuring 1/1000ths of a second for pro sprinters instead of 1/10ths for amateurs).
Secondly, even if they were evenly spaced, the movement between them gets progressivly harder (think 10-minute miles to 5-minute miles).
Thirdly, I think the mix of people changes - from occasional weekend bumblies through to full-time professionals. Once people are in the E6+ arena, they are generally hugely motivated by climbing and also by the aim to get to the next level. Whereas others further down are very happy to bimble on HVS/E1 for the rest of their climbing careers.
Taking the above, I'd suggest that at least the 4th significant figure of your analysis may not be very significant...and probably the third, second and first too!
In reply to Iain Thow:
But some of those people will have climbed harder at some point and John is talking about hardest ever lead as an average, rather than normal lead grade.The 2 are quite different for most people imho
But some of those people will have climbed harder at some point and John is talking about hardest ever lead as an average, rather than normal lead grade.The 2 are quite different for most people imho
In reply to john arran:
Crap methods lead to crap results and so to crap conclusions.
The problem is that there is no data without some dodgy sampling. Despite the large number of users on UKC, I don't think we accurately represent the proportions of 'climbers' out and about. In particular, those who are new or more casual/ less committed, and probably operating at lower grades are less likely to be on here or bother recording routes in logbooks.
Despite those misgivings, speculation can still be interesting.
Crap methods lead to crap results and so to crap conclusions.
The problem is that there is no data without some dodgy sampling. Despite the large number of users on UKC, I don't think we accurately represent the proportions of 'climbers' out and about. In particular, those who are new or more casual/ less committed, and probably operating at lower grades are less likely to be on here or bother recording routes in logbooks.
Despite those misgivings, speculation can still be interesting.
In reply to john arran:
Well I thought it was quite a good effort! Those percentages look as fair estimates as one is likely to get.
Well I thought it was quite a good effort! Those percentages look as fair estimates as one is likely to get.
In reply to john arran:
HVS may be the average life time best of trad climbers in the uk. I could just about believe that I guess. Certainly not the average best if you include all people that climb in the uk IMO (inc indoor climbers etc) prolly more like HS or less as many indoor climbers will never trad climb.
HVS may be the average life time best of trad climbers in the uk. I could just about believe that I guess. Certainly not the average best if you include all people that climb in the uk IMO (inc indoor climbers etc) prolly more like HS or less as many indoor climbers will never trad climb.
In reply to mattrm: Figures from the logbooks would be more meaningful if everyone (who logged) made sure they logged all their routes every time they did them - otherwise distortions occur.
My own logbook is a case in point (although on its own it's not going to change the world) - I've only logged routes where I've got an E point at the time (regardless of the current grade), I've only logged my first lead and/or solo of such routes - 105 climbs. I've not logged the other 3500 routes I've done with probably twice as many repeat ascents as that.
My average logbook grade is probably E1, my average grade of routes I've lead/soloed would probably be VS and the average of ascents I've made (i.e. including repeats) would be lower again because of the number of easy routes I've soloed many times.
There are lies, damn lies and statistics.
As for the OP, interesting idea.
My own logbook is a case in point (although on its own it's not going to change the world) - I've only logged routes where I've got an E point at the time (regardless of the current grade), I've only logged my first lead and/or solo of such routes - 105 climbs. I've not logged the other 3500 routes I've done with probably twice as many repeat ascents as that.
My average logbook grade is probably E1, my average grade of routes I've lead/soloed would probably be VS and the average of ascents I've made (i.e. including repeats) would be lower again because of the number of easy routes I've soloed many times.
There are lies, damn lies and statistics.
As for the OP, interesting idea.
In reply to JJL:
All valid points but my exercise was purely one of fitting a line to guestimated data points and really assumed nothing about grade widths or difficulty of transition. That said, the fact that in fitting the line I had to progressively stretch the proportions as the grades got higher would tally with your second point.
And I'd agree entirely with your error bands - note my guess above that a reasonable error band would be something like 1/3 to 3 times the figures quoted - but that's still far more precise than most of the guesses on the other threads.
All valid points but my exercise was purely one of fitting a line to guestimated data points and really assumed nothing about grade widths or difficulty of transition. That said, the fact that in fitting the line I had to progressively stretch the proportions as the grades got higher would tally with your second point.
And I'd agree entirely with your error bands - note my guess above that a reasonable error band would be something like 1/3 to 3 times the figures quoted - but that's still far more precise than most of the guesses on the other threads.
In reply to LakesWinter:
I know there's a difference between "hardest lead" and "usual grade" (obviously), but still meet a lot of people who "climb VS" and never try anything any harder (at least as a lead). I suspect the total of those people plus the people who "do a bit of climbing" and would max out at Severe or V Diff is much more than a third of all the people climbing.
I know there's a difference between "hardest lead" and "usual grade" (obviously), but still meet a lot of people who "climb VS" and never try anything any harder (at least as a lead). I suspect the total of those people plus the people who "do a bit of climbing" and would max out at Severe or V Diff is much more than a third of all the people climbing.
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